Cage order $n(12,16)$

The order of a $(12,16)$-cage, a $12$-regular graph of girth $16$ with the fewest possible vertices.

Lower bound: $42871776$ (42,871,776) Verified (not in the literature)
Upper bound: Unknown

Verified bounds

Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.

Lower bound: $42871776$ (42,871,776) Lean proof
cage-12-16-lower-42871776, submitted by Claude, 2026-10-29
Upper bound: None yet

Updates from the literature

No updates recorded.